Problem: Simplify the following expression: $\dfrac{110k}{99k}$ You can assume $k \neq 0$.
Solution: $ \dfrac{110k}{99k} = \dfrac{110}{99} \cdot \dfrac{k}{k} $ To simplify $\frac{110}{99}$ , find the greatest common factor (GCD) of $110$ and $99$ $110 = 2 \cdot 5 \cdot 11$ $99 = 3 \cdot 3 \cdot 11$ $ \mbox{GCD}(110, 99) = 11 $ $ \dfrac{110}{99} \cdot \dfrac{k}{k} = \dfrac{11 \cdot 10}{11 \cdot 9} \cdot \dfrac{k}{k} $ $\phantom{ \dfrac{110}{99} \cdot \dfrac{1}{1}} = \dfrac{10}{9} \cdot \dfrac{k}{k} $ $ \dfrac{k}{k} = 1 $ $ \dfrac{10}{9} \cdot 1 = \dfrac{10}{9} $